Paper-sheet processing apparatuses which process paper sheets have been known heretofore. There has been a demand for paper-sheet processing apparatuses each including at least two stacking units for sorting paper sheets such as banknotes to be deposited or withdrawn at a counter of a financial institution such as a bank. Examples of such a paper-sheet processing apparatus include a paper-sheet processing apparatus disclosed in WO 2009/028071, which includes an upper transport mechanism extending in a horizontal direction, a lower transport mechanism extending in the horizontal direction below the upper transport mechanism, and an intermediate transport mechanism provided between the upper and lower transport mechanisms. WO 2009/028071 also discloses that some of the paper sheets transported by the lower transport mechanism are diverted by diverters from the lower transport mechanism and fed to two staking units.